How should students show their work for math word problems?

Someone recently asked me about showing work in math word problems and I thought others might enjoy hearing about this topic also.

Personally, in the lower grades, I'd ask the child to EXPLAIN their thought processes orally, and then gradually teach them to write something on paper. The main thing students in grades 1-3 need to write is the actual calculations they did, not only the final answer.

For example, if they added 23 and 87 to get the answer, they should write 23 + 87 = 110 and include the units of whatever it was, such as $23 + $87 = $110 or 23 cm + 87 cm = 110 cm.

In the upper elementary grades (4-6) I'd like to see students write sentences and/or words in addition to the calculations so that another person can follow their solution.

I'll give some examples.

(from 4th grade)

Mr. Jefferson travels from Paducah to Lexington and back, three times a month. What is his total mileage? (A map shows that the distance in question is 255 miles.)

The purpose of writing down the work allows someone else to follow the person's thought processes. This is of course important for students to learn no matter what their future occupation: they need to be able to explain to others how they solve a problem, whether a math problem or a problem in some other field of life!

One more tip: You could ask a fellow student or sibling to read the student's work to check if it can be followed and understood!

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I got inspired by the blogpost Art School | Geometric Design with Islamic Art where Deborah shows how to make a neat flower design with seven circles, using a compass, and then coloring it using 2, 3, or 4 colors (or however many of your own). I think it ties in neatly with mathematics, and lets students practice drawing circles with a compass.

My girls loved the art/math project. Here are pictures they made:

Here are step-by-step instructions for the flower design:

1. Draw a line and a circle so that the circle's center point is on the line. Then mark the points where this circle intersects the line.

2. Use those points as center points, and draw two more circles. The radius is the same all the time, so make sure you don't change it on your compass!We used 5 cm as the radius, and that made the whole design fit neatly on a regular letter size paper.

3. Now note the two points marked in the picture. They will be used as center points in the next step.